Negative magnetoresistance and hall coefficient of a two-dimensional disordered system

Localization corrections to the longitudinal (δρ) and Hall (δρ_H) resistivities of a two-dimensional disordered system are calculated in all ranges of classical magnetic fields, up to the values at which the mean free path of charge carriers l is less than or of the order of the cyclotron radius R _c. It is shown that the physical reason for the departure of the l dependence of these resistivities from the logarithmic law ∝ ln(l _B /l)) (l _B is the magnetic length) at is the nonlocal process of diffusion in the Cooper channel, rather than the transition to a quasi-ballistic regime. Analytical expressions are obtained that allow one to analyze the interference effect in δρ and δρ_H in quantizing magnetic fields , including the quantum limit. Contrary to popular opinion, the localization corrections to ρ_H are shown to be nonzero. They have a sign opposite to that of the charge carriers and lead to a decrease in the magnitude of the Hall resistivity. Their field dependence has the same features and their relative magnitude is of the same order as in the case of the longitudinal resistivity. The quantum corrections to the Hall resistivity are due to the Larmor precession of the closed paths that electrons follow in the process of their multiple scattering by randomly distributed impurities.